A scaling invariance of the perturbations in $k$-inflation models

Abstract

We study the background and perturbations in $k$-essence inflation models and show that a general $k$-essence exhibits a simple scaling property. In particular, we study two classes of $k$-inflation models with the potential characterized by an inflection point. We demonstrate that these models enjoy scaling properties that could be used to redefine input parameters so that the perturbation spectra satisfy correct normalization at the CMB pivot scale. The background and perturbation equations are integrated numerically for two specific models.

21 pages, 2 figures, 1 table, major revision, Introduction and Sec. 4.4 expanded, one figure added, 13 references added, typos corrected, accepted for publication in Universe